Simplify to lowest terms. $\dfrac{30}{54}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 30 and 54? $30 = 2\cdot3\cdot5$ $54 = 2\cdot3\cdot3\cdot3$ $\mbox{GCD}(30, 54) = 2\cdot3 = 6$ $\dfrac{30}{54} = \dfrac{5 \cdot 6}{ 9\cdot 6}$ $\hphantom{\dfrac{30}{54}} = \dfrac{5}{9} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{30}{54}} = \dfrac{5}{9} \cdot 1$ $\hphantom{\dfrac{30}{54}} = \dfrac{5}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{30}{54}= \dfrac{2\cdot15}{2\cdot27}= \dfrac{2\cdot 3\cdot5}{2\cdot 3\cdot9}= \dfrac{5}{9}$